Robert Pollack (Boston)

will speak on

Slopes of modular forms and the ghost conjecture

Time: 2:00PM
Date: Thu 22nd October 2020
Location: Online [map]

Further information

Abstract: Modular forms are mathematical objects born in complex analysis but in fact have become central objects in number theory. In particular, special modular forms, called eigenforms, have Fourier coefficients which are algebraic integers and these integers contain loads of number theoretic data. In this talk, we will focus on one slice of this data, namely, the highest power of $p$ dividing the $p$th Fourier coefficient (called the slope of the form). Through many numerical examples, we will discuss the properties of these slopes and ultimately state the so-called 'ghost conjecture' which predicts them in a combinatorial way.

(This talk is part of the Algebra and Number Theory series.)

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